On an integro-differential fractional nonlinear Volterra-Caputo equation
S. Guemar1, H. Guebbai2, S. Lemita3
1Université Yahia Fares Médéa. Pôle urbain, Médéa, Algérie
2University of Guelma, Guelma, Algérie
3'Ecole Normale Supérieure de Ouargla, Cité Ennacer, Ouargla, Algérie
Keywords: Volterra equation, integro-differential-fractional equation, fixed point, nonlinear equation, product integration method
Abstract
In this paper, we study a nonlinear integro-differential Volterra equation with a fractional Caputo derivative. Based on techniques derived from a study of classical Volterra equations, namely Picard's iterative sequence and the product integration method, we propose a complete analytical and numerical study of this equation. Our study is closed by the development of two numerical examples.
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